Abbreviation：
S - Strong signals
WC - Weak but correlated signals
WI - Weak and independent signals
FS - Forward selection
spe - specificity
sen - sensitivity
eg: ‘SLASSOspe’ stands for the specificity of selecting strong signals by LASSO.
Definition of strong signals — \[S_1=\{j:|\beta_j|>c\sqrt{log (p) / n},\mbox{ some } c>0, 1\le j \le p\}\]
Definition of weak-but-correlated signals — \[S_2=\{j: 0<|\beta_j|\le c\sqrt{log (p) / n},\mbox{ some } c>0, \mbox{corr}(X_j, X_j')\ne 0, \mbox{for some } j'\in S_1, 1\le j \le p\}\]
Definition of weak-and-independent signals — \[S_3=\{j: 0<|\beta_j|\le c\sqrt{log (p) / n},\mbox{ some } c>0, \mbox{corr}(X_j, X_j')= 0, \mbox{for all } j'\in S_1, 1\le j \le p\}\]
\[\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2\]